A finite element model for cryosurgery with coupled phase change and thermal stress aspects

The process of freezing in a capillary porous medium is numerically simulated with regard to temperature and stress fields with consideration of phase change in the context of cryosurgery applications. Using a transformation of the principal field variable into a new one, the so-called freezing index, the bioheat transfer equation with a phase change is converted into a form that is readily amenable to a standard finite element solution based on a fixed mesh, thereby circumventing the numerical difficulties associated with the moving boundary problem. The temperature-dependent mechanical equilibrium equation is then solved in a quasi-static manner to analyze the resulting thermal stresses and deformations. Using the developed finite element model, a multiprobe cryosurgery for prostate cancer treatment is simulated in detail based on a real prostate geometry together with the actual cryoprobe placements and the freezing protocol used during surgery. The numerical results are then discussed and provide both quantitative and graphical support to prostate cryosurgery planning.